Global solutions to a two-dimensional chemotaxis-Euler system with robin boundary conditions on oxygen

TL;DR

This paper proves the global existence and uniqueness of solutions for a 2D chemotaxis-Euler system with physical boundary conditions, under small initial oxygen concentration.

Contribution

It establishes the first global well-posedness result for this chemotaxis-Euler system with Robin boundary conditions in two dimensions.

Findings

Unique global solution exists under small initial oxygen concentration.

The system is well-posed with physically relevant boundary conditions.

Results contribute to understanding chemotaxis models with fluid dynamics.

Abstract

This paper is concerned with the global well-posedness of a chemotaxis-Euler system in bounded domains of $\mathbb{R}^2$. Completing the system with physical boundary conditions, we show that the corresponding initial boundary value problem admits a unique global solution provided that the initial oxygen concentration is suitably small.